Nonlinear Flow Toward Wells

Abstract

A comprehensive review of the validity of Darcy's law is presented with the emphasis on the necessity for a nonlinear flow law for Reynolds numbers especially greater than one. Subsequently, the nonequilibrium formula is developed for nonlinear flow and is useful in determining either the aquifer parameters from the time drawdown observations or in predicting the drawdown variations in a confined aquifer tapped by a fully penetrating well. The derivation of the necessary formula is based on the continuity equation in terms of the specific yield and a nonlinear flow law which is adopted in this paper as the exponential law. The general solution of nonlinear flow toward wells reduces to the Theis nonequilibrium equation when the turbulence exponent is taken as equal to one. Initial and moderate portions of nonlinear flow type curves prove to be very important for the estimation of aquifer parameters, especially for the turbulence exponent and for the nonlinear flow transmissivity. It is observed that even in the same aquifer with a constant pump discharge, differences in the observation well distances to the main well give rise to different type curves. The late time drawdown data can be used only for determining the conventional linear flow related parameters such as the storativity and the transmissivity. Finally, the application of the methodology has been performed for some field data available in the literature.